Bessel vortices in spin-orbit-coupled binary Bose–Einstein condensates with Zeeman splitting

Huan Bo Luo, Boris A. Malomed, Wu Ming Liu, Lu Li

Research output: Contribution to journalArticlepeer-review


We present an analysis of stationary solutions for two-dimensional (2D) Bose–Einstein condensates (BECs) with the Rashba spin–orbit (SO) coupling and Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system can be solved exactly. The solutions are semi-vortices of the Bessel-vortex (BV) and modified Bessel-vortex (MBV) types, in the presence of the weak and strong Zeeman splitting, respectively. The ground states (GSs) of the full nonlinear system are constructed with the help of a specially designed neural network (NN). The GS of the mixed-mode type appears as cross-attraction interaction increases. The spin texture of the GS is produced in detail. It exhibits the Néel skyrmion structure for the semi-vortex GS of the BV type, and the respective skyrmion number is found in an analytical form. On the other hand, GSs of the MBV and mixed-mode types do not form skyrmions.

Original languageEnglish
Article number106769
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Dec 2022


  • Bessel vortices
  • Neural network
  • Spin–orbit coupling
  • Zeeman splitting


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